McHale surprises to take the first set
The American had scored wins over Kiki Bertens and Naomi Osaka in the previous two rounds, but she was in immediate danger, Svitolina setting up double break point with a deft forehand volley.
After saving the first break chance, McHale dumped a backhand into the net, giving the Ukranian a quick 3-1 lead. The American immediately answered, capping a long game that featured three deuces with a break back.
The rallies continued to be long and at break point in the ninth game, it was McHale who angled off a backhand, forcing an error from Svitolina to achieve the lead at 5-4.
After building a 40-0 lead while serving for the set, she need all three of those chances and another exhausting rally saw the American's final forehand limply returned, giving her the opening set.
Svitolina wins break-filled second set
It was another fast start for the seventh seed as she immediately took the lead, breaking after more exhausting rallies when McHale's backhand was well long. A hold consolidated Svitolina's break to give her a 3-0 lead.
Once again, it was McHale finding her way back into the match straightaway and she was back on serve, taking the offensive and pushing the seventh seed around before a putaway forehand delivered the set back to parity.
After another exchange of breaks, it was Svitolina who finally got the upper hand, ripping a forehand winner to cap a 24-shot rally and level the match at one set all.
Svitolina takes decisive set
This time, it was McHale on the front foot, breaking to open the deciding set, only to see Svitolina respond with a break of her own. After each player held, the Ukranian made the decisive move.
Trailing 3-2, McHale's steady ground game suddenly went awry, three straight unforced errors handing Svitolina the break and after the seventh seed held, she took a commanding 5-2 lead.
It was a hold for the American to cut the deficit to 5-3, forcing Svitolina to serve out the match, which she did so when McHale flew a final forehand long, bringing a conclusion to a two-hour, 24-minute match, Svitolina advancing to face Lauren Davis in the quarterfinals.